[tex]\sf2x+3y=-9[/tex]
Convert to slope-intercept form, y = mx + b.
[tex]\sf2x+3y=-9[/tex]
Subtract 2x to both sides:
[tex]\sf3y=-2x-9[/tex]
Divide 3 to both sides:
[tex]\sf~y=-\dfrac{2}{3}x-3[/tex]
Now it's in slope intercept form, y = mx + b where 'm' is the slope. So the slope here is -2/3, which is Negative.
[tex]\sf~y=3x-6[/tex]
This is already in slope intercept form. So the slope here is 3, which is Positive.
For #3 and #4, take any two points from the table and plug them into the slope formula.
[tex]\sf~m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Let's take (0, 7) and (1, 5).
x1 y1 x2 y2
[tex]\sf~m=\dfrac{5-7}{1-0}[/tex]
Subtract:
[tex]\sf~m=\dfrac{-2}{1}[/tex]
Divide:
[tex]\sf~m=-2[/tex]
So the slope is negative.
For #4, let's take (2, -8) and (3, -7)
x1 y1 x2 y2
[tex]\sf~m=\dfrac{-7-(-8)}{3-2}[/tex]
Subtract:
[tex]\sf~m=\dfrac{1}{1}[/tex]
Divide:
[tex]\sf~m=1[/tex]
So the slope is positive.
